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Turbidity measurement is important for water quality assessment, food safety, medicine, ocean monitoring, etc. In this paper, a method that accurately estimates the turbidity over a wide range is proposed, where the turbidity of the sample is represented as a weighted ratio of the scattered light intensities at a series of angles. An improvement in the accuracy is achieved by expanding the structure of the ratio function, thus adding more flexibility to the turbidity–intensity fitting. Experiments have been carried out with an 850 nm laser and a power meter fixed on a turntable to measure the light intensity at different angles. The results show that the relative estimation error of the proposed method is 0.58% on average for a four-angle intensity combination for all test samples with a turbidity ranging from 160 NTU to 4000 NTU.
© 2015 Optical Society of America
1. Introduction
Turbidity is defined as the reduction in the transparency of a liquid sample caused by the presence of undissolved matter [1] and is a direct indicator of water quality. Turbidity measurement plays a crucial role in industrial, medical, and scientific research, e.g., water quality assessment, the monitoring of watershed conditions [2], cell culturing, and research on nutrients and bacteria [3,4].
Quantitative measurement of the turbidity dates back to 1900 when Whipple and Jackson [5] developed the Jackson candle turbidimeter, where light from a candle flame is transmitted through the water sample, and the intensity of the transmitted light is compared with a standard suspension of diatomaceous earth [6]. Nowadays, the turbidity of a water sample is determined by comparing either the transmitted light (e.g., in transmissometers) or the scattered light (e.g., in nephelometers) of the water sample with that of a standard suspension.
In transmissometers, the intensity of the transmitted light is measured (as shown in Fig. 1(a) with the angle θ = 0°), and the attenuation coefficient of the sample is estimated according to the Beer–Lambert law [7]. The turbidity of the sample is then considered to be identical to that of a standard formazin suspension with the same attenuation coefficient. Because the intensity of the transmitted light exponentially decreases with respect to the turbidity (illustrated in Fig. 1(b) with θ = 0°), as proven in ISO 7027 [1], the transmissometer can achieve a high accuracy over a moderate range. However, the scattering in the light path is severe for a high turbidity (e.g., >1000 NTU), and the light intensity at θ = 0° becomes so weak that the measurement is very sensitive to the noise in the sensor system. In addition, multiple scattering occurs at a high turbidity along with direct scattering, which increases the difficulty of the turbidity measurement even further [6]. When measuring the turbidity up to 10,000 NTU with a commercial transmissometer, the uncertainty can be as large as ±10% [8].
Fig. 1 (a) Schematic of the turbidity measurement. A transmissometer only collects the intensity of the transmitted light (i.e., θ = 0°) to measure the turbidity, whereas a nephelometer collects the scattered light at scattering angles θ other than 0°. (b) Qualitative illustration of the relationship between the light intensity and the turbidity for θ = 0°,30°,90°, and 135°. Each curve is normalized to its maximum value.
Because the sensitivity of the light intensity to the turbidity varies with the measurement angle θ, nephelometers collect the scattered light at scattering angles θ other than 0°. For instance, a high accuracy has been achieved for the turbidity estimate by measuring the scattered light at 90° in low-turbidity cases and at 140° in high-turbidity cases [9–11 ]. Barter [12] compared five commercial nephelometers (with θ = 90°) and found strong agreement under low-turbidity conditions, where the turbidity has a linear relationship with the scattered light intensity at 90°. However, there is a notable deviation between the values measured by different devices when the turbidity is higher than 400 NTU. To correct the nonlinear trend at high turbidity levels, more detectors are used to acquire information from different scattering angles. Numerical formulas (i.e., fitting functions) are built to relate the turbidity of the sample and the scattered light intensity (or a combination of light intensities scattered from different angles) during calibration. A commercial turbidimeter uses a combination of scattered light at {0°,30°,90°,138°} to estimate the turbidity with the so-called ratio method [13]. In its algorithm, the light intensity at 90° is divided by a weighted sum of the light intensities at {0°,30°,90°,138°} to achieve an accurate fit between the turbidity and intensity measurements, even in the case of multiple scattering, intensity fluctuations in the light source, or drifting in the sensor [6].
In this paper, a generalized weighted ratio method is proposed to further improve the accuracy of the turbidity estimate over a wide range, where the turbidity is represented as the ratio of the weighted sum of the scattered light intensities measured at a series of angles. The structure of the fitting function has been expanded, thus adding flexibility to the fitting between the turbidity and intensity measurements. The weight of each light intensity is calibrated from formazin solutions with a known turbidity. An optimal combination of scattered light intensities is selected. The proposed method exhibits a significant improvement in the estimation accuracy for turbidities from 160 NTU to 4000 NTU.
The main contribution of this paper is the exploration of the numerical relationship between the turbidity and the multi-angle scattered light intensities, which leads to a higher accuracy both theoretically and in experiments. According to an analysis of the measurement results, more insight can be gained to improve the understanding of particle scattering in water.
The paper is structured as follows. The principles of turbidity estimation are introduced in Section 2. In Section 3, the proposed generalized weighted ratio method for turbidity measurement is presented with a detailed algorithm. The experimental setup and experiments are described in Section 4, followed by the results in Section 5. A discussion is presented in Section 6, and the paper is concluded in Section 7.
2. Principles of turbidity estimation
2.1. Light propagation and turbidity
When light propagates through a water sample, its energy is attenuated by absorption and scattering. According to Kirk [14], the radiant flux exponentially decreases along the propagation path as
where Φi and Φt denote the radiant fluxes of the incident light before and after attenuation, respectively; c is the attenuation coefficient given by c = a + b (a is the absorption coefficient, and b is the scattering coefficient); and r is the propagation distance.The total effect of scattering is described by the scattering coefficient b, whereas the angular distribution of scattered light is described by the volume scattering function (VSF). Referring to Fig. 2, the VSF β(ψ) is defined as
where Φs(ψ) is the scattered power in the direction of ψ. Δr and ΔΩ represent the changes in the distance and solid angle, respectively. Physically, the VSF describes the angular scattering per unit distance Δr and unit solid angle ΔΩ. Assuming azimuthal symmetry [16], b is the integral of β(ψ) in all directions:Fig. 2 Definition of the volume scattering function (VSF; from [15]), where Φi,Φa,Φs, and Φt denote the radiant fluxes of the incident light, absorbed light, scattered light, and transmitted light, respectively. ΔA is the area onto which the incident light is projected. ΔV is the volume of water that is illuminated by the incident light. The medium is assumed to be isotropic, and the light is assumed to be unpolarized; therefore, the scattering process is azimuthally symmetric so that the shape of the VSF depends only on the scattering angle.
On the basis of a, b, and β(ψ), the optical properties of a water sample due to the particles in the sample can be well-defined.
Because the direct measurement of a, b, and β(ψ) is difficult and often impractical for in situ cases [14, 17–21 ], the turbidity has been introduced as an alternative to measure the effect of undissolved particles on the incident light. An artificial definition of a standard suspension’s turbidity is used to describe the turbidity of natural water samples. For example, the formazin (C2H4N2) suspension is a standard suspension, in which the randomness of particle shapes and sizes features remarkable statistical reproducibility and fits a wide range of possible particles that can be found in real-world samples [6]. The turbidity of the formazin stock I suspension is defined as 4000 NTU, which is prepared by quantitatively mixing 5.0 g of hexamethylenetetramine (C6H12N4) and 0.5 g of hydrazine sulfate (N2H6SO4) in 1000 ml of filtered water and leaving it for 24 h at 25 ± 3 °C. Calibration suspensions with other turbidities can be obtained by diluting the formazin stock I suspension [1].
2.2. Turbidity estimation methods
2.2.1. Estimation from transmitted light
For a given light source, the intensity of transmitted light (see Fig. 1, with θ = 0°) exponentially decreases with the turbidity of the sample as
where T denotes the turbidity of the sample, I 0 denotes the measured transmitted light intensity, and m and n are parameters determined during calibration. The turbidity of the sample is calculated as2.2.2. Estimation from scattered light at θ = 90°
For a low turbidity, the scattered light intensity at θ = 90° changes linearly with respect to the turbidity [6]. Therefore, the light intensity at 90° can be measured to determine the turbidity as well. The analytical formula is given by
where I 90 is the scattered light intensity at 90°, and k 1 and k 2 are parameters determined during calibration. Equation (6) is a typical linear equation that needs only two sets of T and I 90 to establish two equations to determine k 1 and k 2. In practice, k 1 and k 2 are determined from more than two sets of T and I 90 by the the linear least-squares method in order to reduce the influence of measurement noise. After k 1 and k 2 are calibrated, Eq. (6) is used to estimate T from I 90.2.2.3. Multi-angle estimation method
For samples with a high turbidity, the scattered light intensity at 90° no longer has a linear relationship with the turbidity [6]. Scattered light from multiple angles can be used for turbidity estimation as well. For example, in the ratio method [13], four sensors are set at 0°, 30°, 90°, and 138° with respect to the incident light, i.e., θ = {0°,30°,90°,138°}. The turbidity is related to the measured intensity as
where {I 0,I 30,I 90,I 138} represent the scattered light intensities at the angles of {0°,30°,90°,138°}, respectively; and {k 1,k 2,k 3,k 4} are the weight coefficients to be determined. The denominator of Eq. (7) is the weighted sum of the intensities with the weights of {k 1,k 2,k 3,k 4}. In this case, at least four sets of T and {I 0,I 30,I 90,I 138} from a standard formazin suspension are required to determine the parameters k 1, k 2, k 3, and k 4. Since information is collected from four angles to estimate the turbidity, the range of measurement is extended, and the accuracy is improved compared with the estimate from a single angle.3. Generalized weighted ratio (GWR) method
On the basis of Eqs. (6) and (7), the algorithms used for turbidity estimation can be generalized as
where the vector I = {I 1,I 2,…,Ip} represents the scattered light intensities at p different angles (i.e., θ 1,θ 2,…,θp), and the vector K = {k 1,k 2,…,kq} represents a series of parameters, where q is the number of parameters. The function f maps T from I. For the ratio method, f is structured as given in Eq. (7) with p = 4, I = {I 0,I 30,I 90,I 138}, K = {k 1,k 2,k 3,k 4}, and q = 4. The denominator in Eq. (7) is the weighted sum of the light intensities at 0°,30°,90°, and 138°; the numerator is the light intensity at 90°.Numerically, the turbidity can be estimated as a data-fitting problem. More flexibility in the function structure generally leads to a lower fitting error. Therefore, a generalized weighted ratio (GWR) method is proposed, and the turbidity is represented as
where {I 1,I 2,…,Ip} are the scattered light intensities at the angles of {θ 1,θ 2,…,θp}, respectively; and are parameters to be calibrated. Compared with Eq. (7), the function structure in Eq. (9) is more generalized because the numerator is not limited to I 90; light intensities from all angles are treated equally without discrimination. The angles for the light intensity measurements (and the numbers of angles) can be optimized to achieve a balance between the estimation accuracy and the complexity of the hardware and software.Because the parameters should not all be zero simultaneously, let k 1 ≠ 0, the numerator and denominator of Eq. (9) be divided by k 1, and Eq. (9) be simplified as
where , . Thus, only the parameters {k 2 k 3,…,k 2 p} need to be calibrated.To determine {k 2,k 3,…,k 2 p} from Eq. (10), the linear least-squares method can be applied as follows. Equation (10) can be rewritten as
For simplicity, is written as and Eq. (11) is represented in vector form as
Suppose that there are M sets of T and {I 1,I 2,…,Ip}, which means M different samples are used for calibration. For the mth sample (m = 1,2,…,M), the turbidity is denoted as Tm, and the scattered light intensities at the angles of {θ 1,θ 2,…,θp} are denoted as I 1, m,I 2, m,…,Ip,m.
Then, M equations can be formed and presented in a matrix form as
and simplified as the matrix equation where A ∈ ℝM× (2 p −1) is a coefficient matrix with each element from the calibration data of T and {I 1,I 2,…,I 2 p}. The vector K ∈ℝ2 p− 1 is unknown and is determined during calibration. The vector B ∈ ℝM is a coefficient vector built from T. If M ⩾ 2p − 1 (i.e., the number of calibration datasets is more than the number of unknown parameters), then the columns of A can be considered linearly independent in practice. The vector K can be estimated as where is the estimate of K with . The turbidity can be estimated as where is the turbidity estimate.In order to evaluate the accuracy of the turbidity estimated by the algorithm, the mean relative error εmean of the estimate is calculated as
where n is the number of samples in the test set, and Ti and are the turbidity and estimated turbidity, respectively, of the ith sample. The maximum relative error εmax among the n test samples is used as a subsidiary index of the accuracy to reflect the reliability of the estimation.Since both sides of Eq. (11) have been divided by the intensity I 1, the measurement noise, or more precisely, the signal to noise ratio in I 1 has significant influence on the accuracy of the estimate . Therefore the angle θ 1 is referred to as the extraordinary angle in this paper, while other angles (i.e., θ 2,…,θp) are ordinary angles. Change in the order of the ordinary angles doesn’t have any influence on accuracy of the estimate, but the selection of the extraordinary angle makes difference. For instance, {90°,0°,30°,135°} and {90°,135°,0°,30°} result in the same estimate of T, while {90°,0°,30°,135°} and {0°,90°,30°,135°} can lead to different . In search for the optimal angle combination later in Section 5.2, each angle has been set as the extraordinary angle once to get an optimal fitting between T and {I 1,I 2,…,Ip}.
4. Experiments
An experimental setup has been built to verify the proposed GWR method. As shown in Fig. 3, the setup includes a turntable, laser source, and power meter. The electronically controlled turntable (RSA200, Zolix, China) is fixed on a breadboard and is controlled by a computer with LabVIEW (NI, USA). The repeat positioning uncertainty of the turntable is less than 0.005°. A power meter (FieldMaxII-TO, Coherent, USA) matched with a silicon photoelectric diode sensor (OP-2 VIS, Coherent, USA) is used to measure the scattered light power (or radiation flux), and the light power (W) is used to represent the radiation intensity in the experiment. The sensor of the power meter is fixed on the turntable and rotated around the center of the turntable. Because lasers are sensitive to changes in the turbidity of the samples [22], an 850 nm laser (CPS850S, THORLABS, US) is used as the light source. A sample holder is fixed to the center of the turntable. The laser and sensor are adjusted to be on the same horizontal plane. The whole setup is shielded from environmental variations using shading plates.
Fig. 3 Top view (left) and side view (right) of the experimental setup. An 850 nm laser is used as the light source. A power meter is fixed on a turntable to collect the scattered light intensity at a series of angles. The intensity is collected as the turntable is rotated in intervals of 5°.
As per ISO 7027 and Barter [12], the formazin stock I suspension (4000 NTU) is diluted with reverse-osmosis-purified water (with a resistivity of more than 18 MΩ·cm at 25 °C) in the lab by using pipettes (Thermo Scientific Finnpipette Colour 100–1000 µl, Thermo Fisher Scientific, USA) and 25 ml volumetric flasks to obtain suspensions with turbidities of 160–4000 NTU in equal intervals of 160 NTU (see Table 1). In total, 25 samples are prepared for the experiments; 15 samples (in roman, e.g., 160) are used to calibrate the parameters, and 10 (in boldface and underlined, e.g., 320) are used for the test.
Table 1. Turbidities of the standard formazin solutions used as samples. The boldfaced and underlined values (e.g., 320) are the turbidities of the samples for tests. The others (e.g., 160) are for the calibration.
In the experiment, all of the cuvettes of the samples are mixed by gentle agitation and inversion before measurement. Careful attention is paid to avoid entrainment of air bubbles within the sample. Each sample is measured for less than 2 min, and the average of three measurements is taken for every sample to reduce the random measurement noise. The scattered light is collected every 5° with the turntable. Because of the sensor shade, the range of measurement is limited to 0°–150°.
During the experiments, 25 samples are used. For each sample, the scattered light intensities at 31 angles (every 5° from 0° to 150°) are recorded in the matrix I ∈ℝ25 × 31. The standard turbidities of the samples are recorded in the vector T ∈ ℝ 25. The data are divided into the calibration and test sets, as presented in Table 1.
5. Experimental results
5.1. Light powers at different turbidities and angles
Figures 4(a) and 4(b) show the light powers at different turbidities and angles, as measured with the experimental setup. The light power distribution is saddle-shaped with its peak at a low turbidity and small angle. In general, the light power decreases as the turbidity or angle increases throughout the measurement range.
Fig. 4 Light power distribution for various turbidities and measurement angles: (a) 3D view and (b) contour plot. The highest light power appears at a low turbidity at small angles, and the smallest light power appears at a low turbidity at large angles.
Figure 5(a) shows the angular distribution of the scattered light power for different turbidities. For a turbidity between 160 and 1920 NTU, the light power decreases from 0° to about 120° and then increases. The maximum light intensity is at 0°, and most of the light power is distributed at forward angles. There is also a change in the shape of the curve as the turbidity increases. For a turbidity between 1920 and 4000 NTU, the maximum light intensity is at 150° within the measurement range (and may be even greater at a larger angle, as the capabilities of the experimental setup are limited). The increase in the turbidity clearly causes the light power to shift from small forward angles to backward angles, which indicates that backward angles are important for high-turbidity estimation.
Fig. 5 Light intensity changes with respect to different angles and turbidities. (a) Angular distribution of the scattered light intensity for different turbidities. (b) Relationship between the light intensity and the turbidity. It can be seen that the light scattered from different angles is sensitive to the variation in the turbidity in different regions.
As shown in Fig. 5(b), the light intensity varies with the turbidity in a different manner for different measurement angles. For small angles such as 0°–20°, the light intensity decreases almost exponentially with respect to the turbidity. Moreover, the scattered light intensity at 0° is weak when the turbidity is more than 1000 NTU. For angles between 30° and 90°, the light intensity first increases with the turbidity and then decreases, with the peak shifting from 320 NTU to 1760 NTU. For angles from 90° to 110°, the light intensity linearly increases to about 2000 NTU and remains almost constant with little fluctuation because of multiple scattering and strong attenuation [6]. For angles between 110° and 150°, the light intensity keeps increasing from low to high turbidity. This suggests that transmissometers are more appropriate for a low turbidity, and the light from large backward angles is helpful for high-turbidity estimation.
5.2. Turbidity estimation with the GWR method
Because the accuracy of the turbidity estimate by the GWR method depends on the angle combination, the estimation error is evaluated for all possible angle combinations, and the combination with the lowest relative estimation error εmean is selected. Two to six angles are used for turbidity estimation (i.e., p = 2,3,…,6). The procedure for determining the optimal angle combinations for the GWR method is summarized as follows (see Algorithm 1.
Algorithm 1 Procedure for determining the optimal angle combinations for the GWR method
Table 2 lists the angle combination leading to the minimum value of εmean. The second and third minimum values of εmean are also listed for reference. With the GWR method, the minimum value of εmean dramatically decreased from 4.63% to 1.19% when the number of angles increased from two to three. It continued to decrease to 0.58% when four angles were used and to 0.51% with five angles. The minimum value of εmean reached 0.46% with six angles. The line with the circles in Fig. 6(a) clearly illustrates the trend in the minimum value of εmean. Because there is no significant improvement in the turbidity estimate for p > 4, we considered the four-angle combination to be adequate for turbidity estimation in terms of the accuracy and complexity.
Table 2. Best angle combinations and εmean of the three best combinations with two to six angles. The boldfaced column represents the minimum value of εmean.
Fig. 6 Comparison between the ratio and GWR methods. (a) Mean relative errors for different methods. (b) Relative error of each sample in the test set. The marked plus sign and circle in (a) indicate the average values of the dashed lines with inverted triangles and plus signs in (b), respectively. When three or more angles are used, the minimum value of εmean of the GWR method is less than that of the ratio method.
The accuracies of the proposed GWR method and existing ratio method are compared in Fig. 6(a). Since there is little difference between the scattered light intensities at 138° and 135° in our experiment, the angle around 138° in the ratio method is specified as 135° in this study for convenience. The value of εmean for the ratio method is 1.8%, whereas that for the GWR method reached 0.58% with four angles (i.e., 30°, 5°, 145°, and 150°). Figure 6(b) shows the relative error of the turbidity estimate point by point. The GWR method results in smaller relative errors for most of the tested samples. Even when the same four angles as the ratio method are used (i.e., 0°, 30°, 90°, and 135°), the GWR method still produces a lower relative error (i.e., 1.29% compared to 1.80%), which benefits from the flexibility of the structure of the fitting function in Eq. (10).
6. Discussion
6.1. Uncertainty in the formazin suspension
During the preparation of water samples, the uncertainty in the precision impacts the ground truth of the turbidity. The turbidity of the diluted standard formazin suspension is given as
where T 0 denotes the turbidity of the original standard formazin suspension (i.e., T 0 = 4000 NTU), and Td denotes the turbidity of the sample after dilution. Vd denotes the volume of the volumetric flask with Vd = 25 ml, and V 0 = 1,2,…,25 ml denote the volumes of formazin needed to prepare the 160 NTU, 320 NTU,…, 4000 NTU samples, respectively.The uncertainty in Td mainly comes from the uncertainties in V 0 and Vd. For small variations in V 0 and Vd (denoted as ΔV 0 and ΔVd, respectively), we have
where ΔTd is the uncertainty in and are the partial derivatives of Td with respect to V 0 and Vd, respectively.The uncertainty of the pipette is ±5.00 µl for delivering a 1000 µl suspension. When the pipette is used s times to prepare a sample with a certain turbidity, we have Td = s·160 NTU and ΔV 0 = s·0.005 ml (s = 1,2,…,24). The uncertainty of the 25 ml volumetric flask is ΔVd = 0.03 ml. Then, the relative resulting uncertainty can be calculated as
Therefore, the maximum uncertainty of the diluted samples is 0.62% when a sample with a turbidity of 160 NTU is diluted (i.e., s = 1), and the minimum uncertainty is 0.50% when a sample with a turbidity of 3840 NTU is diluted (i.e., s = 24). The mean uncertainty for all samples is 0.52%.
6.2. Frequently appearing angles
To investigate the relationship between the angle combination and the turbidity estimation accuracy, the frequencies of angle appearance in the best 100 combinations (with small values of εmean for a four-angle combination) are summarized in Fig. 7.
Fig. 7 Frequency of angle appearance in the first 100 combinations with the minimum mean relative error. The frequency is counted every 10°, e.g., 0° on the abscissa represents 0° and 5°, and 10° on the abscissa represents 10° and 15°.
It can be seen that most frequently appearing angles fall into two groups: forward angles in the range of 0°–40° and backward angles in the range of 90°–140°. The reasons for this can be deduced from Fig. 5. The light intensity at 0°–10° is large in magnitude, has good monotonicity, and has a high sensitivity to the turbidity when turbidity is low or moderate. The intensity at 20°–40° becomes less sensitive to a change in the turbidity but still provides an adequate signal strength for a reliable estimate. For angles between 50° and 80°, fluctuations can be observed in the intensity–turbidity curve, which causes greater difficulties during data fitting with the ratio function, and a large estimate error can occur. As backscattering becomes significant for a high turbidity, the backward angles (e.g., 90°–150°) become more important. Therefore, an appropriate combination of angles in Groups I and III can result in an accurate turbidity estimate over a wide range.
6.3. Field-of-view (FOV) of the sensor
The geometrical configuration of the sensor and the water sample in the experimental setup is depicted in Fig. 8. The active area of the sensor collects the photons scattered from the water sample within an angle of about 23.6°, i.e., FOV of the sensor. By sophisticated design of the setup, the FOV of the sensor can be narrowed, light from different direction of the water sample can be discriminated more precisely and the angular resolution in VSF measurement can be improved. Improvement in the accuracy of the turbidity estimation can be expected as well.
7. Conclusion
In this paper, a GWR method was proposed to accurately estimate the turbidity over a wide range. A detailed algorithm was introduced, and an experimental setup was built to verify the method. The experimental results showed that the proposed GWR method leads to a mean relative estimation error of 0.58% for a turbidity measurement with the optimal combination of four scattering angles.
It should be noted that the optimal angle combination depends on the configuration of the setup (e.g., the FOV of the sensor) and VSF of the water sample (e.g., the shape and size of the particles in the sample). However, it is evident that a four-angle combination indeed improves the accuracy of the turbidity measurement, and the accuracy can be further improved by expanding the structure of the estimation algorithm.
Future work will focus on exploration of the relationship between the turbidity and VSF of the water sample. Standard particles such as polystyrene latex will be utilized to control the shape and size in the sample.
Acknowledgments
This work is supported by the National High-tech R&D Program of China (863 Program) (No. 2014AA093400), National Natural Science Foundation of China (No. 11304278, No. 51120195001), Science Fund for Creative Research Groups of National Natural Science Foundation of China (No. 51221004), Zhejiang Province Commonwealth Technology Research Project (No. 2013C31052), and Open Fund of State Key Laboratory of Satellite Ocean Environment Dynamics (No. SOED1606). The authors express their sincere gratitude to the Ocean Biology group in Lab-106 of Ocean College for their generous help during the sample preparation.
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